So now New York City has approved the so-called “poor door,” a separate entrance for those living in the “affordable housing” part of a 33-story, Upper East Side luxury condo.

Built by Extell, the high-rise will have 219 units renting at market rates, plus 55 units for low-income earners who will pay much less.

The idea that the residents of these latter units will have a separate entrance has set off comparisons to Downton Abbey, where Lord Grantham and his brood live upstairs in sumptuous conditions, while the servants live down below.

But before the howls of the class-warfare crowd grow too loud, they might want to remember that they are the ones who caused this class-based segregation in the first place.

Because it’s precisely their insistence on defining where poor people live that is responsible for poor doors, not to mention the tax breaks for developers and relief from some zoning restrictions.

Here’s how it works: The developers get to throw up a tower of luxury condos or apartments — and often a tax abatement. In return, they agree to sell or rent a certain number of units at highly reduced prices. In this way, city bureaucrats believe they are mixing poor households in with richer ones.

So why the poor door? As The Post’s Steve Cuozzo reported more than a year ago, separate doors are required for this kind of the building. In part to make it easier down the road for the units to be managed separately by a non-profit.

How much better and simpler it would be if the city did two things. First, just make it easier to build housing of any type. Second, give those who need subsidies vouchers they can use anywhere rather than assign them to a particular unit.

Mayor de Blasio is right: There is a huge crisis in affordable housing in our city. But that’s because demand far outstrips a supply that is limited by regulations that make it expensive to build and by a housing market in which nearly half of all apartments are subsidized.

Even if builders build just luxury units, when supply is expanded, people move up.

That means an apartment that was once luxury becomes middle class, and a middle-class apartment becomes working class, and down the line. If it weren’t put into government-designated buildings and units, we’d have much more mixing.

Next time you hear people complaining about poor doors, remember it’s the government that created them.